Attachment 24112

Pentagon ABCDE

BC = CD = BD = AE

Perimeter (ABCDE) = 10

Find the sides of rectangle, for which the area of the pentagon will be maximum.

Please help! i need it so much

(sry for my english)

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- Jun 19th 2012, 11:28 AMTeloPentagon Problem
Attachment 24112

Pentagon ABCDE

BC = CD = BD = AE

Perimeter (ABCDE) = 10

Find the sides of rectangle, for which the area of the pentagon will be maximum.

Please help! i need it so much

(sry for my english) - Jun 19th 2012, 12:08 PMrichard1234Re: Pentagon Problem
Let and . The area of triangle BCD is , and the area of ABDE is . Hence the area of the pentagon P is

However you know that the perimeter is 10, so . Substitute into the area equation to obtain

Simplify, and differentiate both sides with respect to x and find critical points. - Jun 19th 2012, 12:11 PMTeloRe: Pentagon Problem
the answer is 10/(6-sqr(3)) and (15-5sqr(3))/(6-sqr(3)) but i cant get those answers :(

- Jun 19th 2012, 12:21 PMReckonerRe: Pentagon Problem
Suppose that the vertical sides of the rectangle each have length and suppose that the other sides have length

The area of the pentagon is

and the perimeter is

Substituting this into the area equation above produces

Differentiating,

We locate the critical value:

Now you can find - Jun 19th 2012, 12:28 PMReckonerRe: Pentagon Problem
- Jun 19th 2012, 12:34 PMTeloRe: Pentagon Problem
thanks alot!

- Jun 19th 2012, 01:24 PMrichard1234Re: Pentagon Problem
@Reckoner whoops. Can't do math in my head anymore lol. I just fixed my original post.